Such a chuck is known from DE 299 22 642 [U.S. Pat. No. 6,419,430], in which the claws are pivoted about an axis by means of the gripper head for displacement between an open position and the holding position. This chuck has proved effective in practice, but in order to produce sufficient gripping force it requires relatively large axial displacement of the gripper head, this being associated with a correspondingly long construction of the chuck.